80 Section 6: Statistics FunctionsLinear Estimation

With two-variable statistical data accumulated in the statistics registers, you can estimate a new y-value( yˆ ) given a new x-value, and estimate a new x-value( xˆ ) given a new y-value.

To calculate yˆ :

1.Key in a new x-value.

2.Press gR.

To calculate xˆ :

1.Key in a new y-value.

2.Press gQ.

Example: Using the accumulated statistics from the preceding problem, estimate the amount of sales delivered by a new salesperson working 48 hours per week.

Keystrokes

Display

 

48gQ

28,818.93

Estimated sales for a 48 hour

 

 

workweek.

The reliability of a linear estimate depends upon how closely the data pairs would, if plotted on a graph, lie in a straight line. The usual measure of this reliability is the correlation coefficient, r. This quantity is automatically calculated whenever yˆ or xˆ is calculated; to display it, press ~. A correlation coefficient close to 1 or –1 indicates that the data pairs lie very close to a straight line. On the other hand, a correlation coefficient close to 0 indicates that the data pairs do not lie closely to a straight line; and a linear estimate using this data would not be very reliable.

Example: Check the reliability of the linear estimate in the preceding example by displaying the correlation coefficient.

Keystrokes

Display

 

~

0.90

The correlation coefficient is close to

 

 

1, so the sales calculated in the

 

 

preceding example is a good

 

 

estimate.

To graph the regression line, calculate the coefficients of the linear equation y = A + Bx.

1.Press 0gRto compute the y-intercept (A).

2.Press 1gR~d~-to compute the slope of the line (B).

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